EVALUATION OF DIFFERENT PROBING SYSTEMS USED IN ARTICULATED.pdf

8/10/2019 EVALUATION OF DIFFERENT PROBING SYSTEMS USED IN ARTICULATED.pdf

1/14

Metrol. Meas. Syst., Vol. XXI (2014), No. 2, pp. 233246.

_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Mar. 20, 2013; accepted on Dec. 03, 2013; available online on May. 15, 2014; DOI: 10.2478/mms-2014-0020.

METROLOGY AND MEASUREMENT SYSTEMS

Index 330930, ISSN 0860-8229www.metrology.pg.gda.pl

EVALUATION OF DIFFERENT PROBING SYSTEMS USED IN ARTICULATED

ARM COORDINATE MEASURING MACHINES

Agustn Brau, Margarita Valenzuela, Jorge Santolaria,Juan Jos Aguilar

I3A, University of Zaragoza, Maria de Luna 3, E-50018 Zaragoza, Spain ([email protected])

Abstract

This paper presents a comparison of different techniques to capture nominal data for its use in later verification

and kinematic parameter identification procedures for articulated arm coordinate measuring machines

(AACMM). By using four different probing systems (passive spherical probe, active spherical probe,

self-centering passive probe and self-centering active probe) the accuracy and repeatability of captured pointshas been evaluated by comparing these points to nominal points materialized by a ball-bar gauge distributed in

several positions of the measurement volume. Then, by comparing these systems it is possible to characterize the

influence of the force over the final results for each of the gauge and probing system configurations. The results

with each of the systems studied show the advantages and original accuracy obtained by active probes, and thus

their suitability in verification (active probes) and kinematic parameter identification (self-centering active

probes) procedures.

Keywords: articulated arm coordinate measuring machine, probing systems, self-centering active probe.

2014 Polish Academy of Sciences. All rights reserved

1. Introduction

Due to the increased utilization of AACMMs in the automotive, aerospace, railroad and

energy industries, faster and more reliable calibration and kinematic parameter identification

procedures are constantly sought [13]. A key aspect in this kind of procedures is the process

of capturing data [411]. This data will be compared to nominal distance and position data

obtained from a gauge or some other measurement instrument which functions as a gauge,

thus allowing to define an error objective function to be minimized by means

of a mathematical optimization procedure [7, 1217].

Once the parameters have been identified, the best attainable accuracy in this type

of equipment will greatly depend on the type and number of positions captured by the

AACMM or robot arm [18, 19] and, ultimately, on the extent to which the number

of influences on the capture of points can be minimized. Because the AACMM is a manually-

operated instrument, the results obtained in its verification tests are subject to influences from

the operator, mainly materialized through different probing forces during the data capture

process. These external probing forces cause deformations to the gauge or to the probe

[20, 21] which can result in the loss of accuracy in the verification procedure or during the

process of capturing data for parameter identification.

In this work we present a comparison of the accuracy and repeatability obtained by four

different probing systems (passive spherical probe, active spherical probe, self-centering

passive probe and self-centering active probe), considering that passive probes are the ones

that are dependent only on operators manual capture while active ones are able to

automatically recognize the contact with the measuring object. In addition, the influenceof the probing force over the self-centering passive probe measurements is analyzed through

Unauthenticated

Download Date | 12 14 14 6:30 PM
mailto:[email protected]:[email protected]:[email protected]


2/14

A. Brau,M. Valenzuela, J. Santolaria, J.J. Aguilar: EVALUATION OF PROBING SYSTEMS USED IN ARTICULATED ARM

its components in each of the axis-directions of the sixth reference system of the measurement

arm, showing the advantages of the self-centering active probe in both calibration and

kinematic parameter identification procedures.

2. Methodology

In order to capture the data a ball bar gauge was used to materialize nominal points and

distances in the workspace of an AACMM. The ASME B89.4.22-2004 standard [22], the only

existing standard in the field of AACMM verification, establishes verification procedures

based solely on the capture of points through passive and active spherical tip probes. In this

case, the influence of the probing force over the behavior of the articulated arm has been

analyzed, obtaining the measurement error from the same physical points of the ball bar

gauge through four different probing systems: passive spherical probe, active spherical probe,

self-centering passive probe based on inverse kinematic coupling [7] and self-centering active

probe based on parallel kinematics [23] (Fig. 1). In Fig. 1, the photos in the first row show the

passive spherical probe (left) and active spherical probe (right) and those in the second row

correspond to the self-centering passive probe (left) and self-centering active probe (right).

Fig. 1. Evaluated AACMM probing systems.

In the process of probing the points, a total of 28 spheres have been probed corresponding

to seven different positions of the gauge in a quadrant of the AACMM workspace. From

captured data we have analyzed the combined influence of the probing force and the probing

direction in the final results with each probing system according to the gauge configuration.

Unauthenticated



3/14


3. Data capture setup

There are two ways to express the configuration of an AACMM as a function of the

degrees of freedom of its articulations. The first one is to indicate, by means of three

consecutive numbers, the degrees of freedom of the shoulder, elbow and hand articulations,

respectively. The second one is by defining through a chain of letters each of the possiblerotations of the articulations of the shoulder, elbow and hand. The AACMM used in the

present work is a 7 DOF Platinum series FARO arm with a typical 2-2-3 configuration or

a-b-c-d-e-f-g degrees of rotation (Fig. 1), with a nominal value of semirange of 0.030 mm

obtained in a single-point articulation performance test of the arm manufacturer.

A continuous data capture method has been used for the self-centering probes, and discrete

capture has been used for active and passive spherical probes. The continuous capture

technique allows the massive capture of arm positions corresponding to several points of the

workspace. To this end, a ball-bar gauge of 1.5 m long was placed in 7 positions within the

workspace of the arm in order to cover the maximum number of possible AACMM positions,

to subsequently extrapolate the results obtained throughout the volume. Fig. 2 and Table 1

show the considered positions for the ball-bar in a quadrant of the workspace. The ball-barcomprises a carbon fiber profile and 15 ceramic spheres of 22 mm in diameter, reaching

calibrated distances between the centers with an uncertainty, in accordance with its calibration

certificate, of (1+0.001L) m, with L in mm. In this configuration, 4 spheres of theball-bar in

each of the 7 positions considered are probed, materializing 6 distances between their centers.

Fig. 2. Ball bar gauge test positions and support.

Table 1. List of ball bar gauge positions in quadrant 1.

Position No. Quadrants Tilt Distance B1 Direction

1 C1-C2-C4 Horizontal Medium Tangential

2 C1-C4 Horizontal Near Tangential

3 C1-C2 Horizontal Far Tangential

4 C1 Horizontal Near Radial

5 C1-C2-C4 +45 Medium Tangential

6 C1-C2-C4 -45 Medium Tangential

7 C1 Vertical Medium Tangential

Unauthenticated



4/14


With passive and active spherical tip probes, around 25 points of the sphere surface have

been captured in each measured sphere, while with the self-centering probes around

250 center points have been captured for each sphere (Fig. 3a). For these probes, besides

characterizing the performance of the arm relative to error in distances, its capacity to repeat

measurements of the same point is also tested.

Hence, automatic arm position capture software has been developed to probe eachconsidered sphere of the ball-bar and to replicate the arm behavior in the single-point

articulation performance test, but in this case, to evaluate its repeatability. The rotation angle

values of the arm joints for each position, reached in the continuous probing of each sphere,

are stored to obtain the coordinates of the measured point with respect to the global reference

system for any set of parameters considered. In this way, with the self-centering probes in

contact with the sphere, it is possible to capture the maximum possible number of arm

positions, thus covering a large number of arm configurations for each sphere considered.

The centering of the probe direction with regards to the sphere center is ensured with the

self-centering probes, making this direction cross it (Fig. 3b) for any orientation of the probe.

Thus, it is possible to define in this case a probe with zero probe sphere radius and with

a distance of 22 mm from the position of the housing to the center of the probed sphere,allowing direct probing of the sphere center when the three spheres or planes of the probes

and the sphere of the gauge are in contact. The details of the design, kinematic modeling and

calibration of the self-centering probes is described in [1].

Fig. 3. a) Center points considered for distance error with self-centering probes.

b) Probing the center of a sphere with passive and active self-centering probes.

Unauthenticated



5/14


4. Test and results

In the configuration presented for both groups of probes, results of distance errors

between centers have been obtained for each of the 6 distances materialized in each of the

7 ball-bar positions.

4.1. Spherical tip probes

In the case of passive and active spherical probes, the centers of the spheres were obtained

by means of the least squares method, using the captured surface points. This also allowed us

to obtain both the distance from each probed point to the surface of the sphere and

the standard deviation of this distance. In Fig. 4 the graph shows the error in distance between

the centers of the ball-bar spheres obtained with the active spherical probe against the error in

distance between the centers obtained with the passive spherical probe, relative to

the distances calculated with the ball-bar. With regard to the error in distance, we can observethat the error made with the active probe is slightly smaller than that made with the passive

probe, except in positions 5 and 6. However, it is important to mention that the errors are

almost equal in all positions. Moreover, Fig. 4 shows that most of the final error obtained with

the AACMM in the probing of the spheres is due to the measuring instrument itself with a

very low influence of the probing system chosen in each case. The fact that we get almost the

same error values in the same positions of the ball-bar with different probing systems strongly

suggests that the error map shown in this figure is mainly associated with inadequate values

of the kinematic model parameters, which leads to similar errors in the same positions of the

measured sphere. On the other hand, it is noteworthy that the expected benefit a priori derived

from the use of active probes is not associated with a lesser influence of the probing force, but

simply with a more comfortable capture process. This makes the cost of the active probing

system unjustifiable, compared to the traditional passive probing systems.

Fig. 4. Distance errors of the measured centers.

Fig. 5 shows the difference between the distance errors of active spherical probe and those

of the passive spherical probe in all 42 positions that were used. When a positive difference is

Unauthenticated



6/14


obtained, the active spherical probe error is smaller and thus better than the active spherical

probe, and vice versa when the difference is negative.

Fig. 5. Difference of distance error between active and passive probe.

4.2. Self-centering probes

In the case of the self-centering probes, the mean point of all the captured data for each

sphere was considered as the center of the sphere probed (Fig. 3a). Measured distances for

each sphere in the 7 different positions were compared with the distances obtained with the

ball bar gauge thus obtaining the error in distance (Fig. 6), as well as the differences between

the distance errors of the active spherical probe and the passive spherical probe in all42 positions that were considered (Fig. 7).

Fig. 6. Error in distance of the measured centers.

Unauthenticated



7/14


Fig. 7. Difference of distance error between active and passive probe.

A positive difference represents a smaller error in the active spherical probe and in that

case this probe is considered to be better than the passive one. In the case of positions 3, 4 and

7, three spheres were not measured with the self-centering active probe (sphere 1 in position

3 and sphere 14 in positions 4 and 7)-because the arm was unable to properly reach these

extreme positions with the active spherical probe mounted, so a value of zero was assigned in

the graphs. From Fig. 6, it can be observed that on average, the error made by the

self-centering active probe was less than the one corresponding to the self-centering passive

probe; the errors obtained with the active probe, when greater than those corresponding to thepassive probe, can be associated to the AACMM as it approaches its workspace frontier.

The three-dimensional distances between spheres were obtained calculating the Euclidean

distancejki

D between the mean centers calculated for each sphere, wherejki

D represents the

distance from sphere j to sphere kof ball-bar position i. If0jkD is defined as the nominal

distance between spheresjand kobtained from the ball-bar calibration table, it is possible to

calculate the error in distance between spheresjand kin location ias follows:

0jk jki i ik E D D . (1)

The repeatability error values for all measured points are shown in Fig. 8a and 8b, for the

self-centering active probe and self-centering passive probe respectively.

Unauthenticated



8/14


Fig. 8a. Point repeatability errors for the 7 AACMM positions using the active self-centering probe.

Fig. 8b. Point repeatability errors for the 7 AACMM positions using the passive self-centering probe.

Unauthenticated



9/14


These values represent the errors made in X, Y and Z coordinates of each one of the

approximately 10000 points obtained, corresponding to the 7 positions of the ball-bar gauge

with regards to the mean obtained for each sphere. The repeatability error value for each

coordinate as a function of AACMM joint rotation angles is given by:

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

( , , , , , )

( , , , , , )

( , , , , , )

Xijk ij ij

Yijk ij ij

Zijk ij ij

X X

Y Y

Z Z

. (2)

It can be observed that the error made by the self-centering active probe is much smaller

than the error made by the self-centering passive probe and that in both graphs the error

shows an increment in thezcoordinate. This behavior in thezcoordinate could be explained

by the fact that, unlike what happens in thex andycoordinates, there is no self-compensation

effect in the ball-bar deformation due to the probing force in this coordinate. Figure 9 shows

the magnitude of the error vectors in the direction of the probing forces of every measurement

on the sphere and the resultant of these vectors. As expected, the direction of the resultant

vector (which is multiplied by a module 5 and in red) is downwards which as mentioned

before is caused by lack of the self-compensation effect in the z coordinate.

Fig. 9. Direction and magnitude of error vectors and resultant vector.

In Fig. 10, the standard deviation corresponding to the 7 different positions inx,yandzfor

both types of probes is shown. As expected, the standard deviation in the self-centering

active probe is smaller than that of the one obtained with the self-centering passive probe,

except as mentioned earlier, in the positions were spheres were not measured and a value

of zero was assigned in the graph.

Unauthenticated



10/14


11/14


Fig. 12.X, YandZvalues (mm) expressed in probed points reference system.

For example, the values of the six articulations of the arm in position 1, when the

maximum error exceeds .4 mm, are saved and shown in Fig. 13. This is done by precisely

knowing the maximum and minimum values of the articulations throughout the tests and then

obtaining those articulation values when the error is greater than .4mm. In the present graph,

the range for each articulation in the measuring process is represented by a horizontal line

of the same colour of the sphere being measured. This value was determined by calculating

the mean and one sigma of the standard deviation of the values of Fig. 12 ( 1 ).

Moreover, Table 2 shows the percentage range of angle values for any combination of anglesthat result in an error greater than .4mm. This way, we can analyze the distribution of the

angles that result in an error and observe if there is any pattern in any combination

of articulation values that correspond to an error greater than .4 mm. In this particular

analysis, no pattern could be observed, so most of the probing error could be explained by the

probing force.

Fig. 13. Combination of articulation angles of an AACMM where the maximum error exceeds

4 mm for position 1 of the calibration ball bar gauge.

Unauthenticated



12/14


Table 2. Percentage range for any combination of angle values that result in errors greater than .4mm.

SphereArticulations

1 2 3 4 5 6

B165.44 - 91.16 57.31 - 91.07 3.58 - 24.32 21.08 - 69.15 85.44 - 97.69 47.45 - 100

B6 8.24 - 61.42 72.66 - 91.85 35.09 - 69.70 3.74 - 60.90 23.39 - 58.57 48.56 - 93.32

B100 - 70.44 .069 - 95.83 26.05 - 100 17.68 - 83.02 0 - 81.34 26.18 - 91.30

B1413.88 - 91.70 50.41 - 95.79 22.48 - 82.37 4.14 - 71.10 9.07 - 66.68 33.19 - 83.42

4. Conclusions

In this work, a comparison between four different probing systems applied to capturing

data for parameter identification and verification of an AACMM is presented. Besides the

probing systems traditionally used in the verification of an AACMM, self-centering probing

systems with kinematic coupling configuration and self-center active probing systems have

also been used for the same purpose. Such probing systems are very suitable for use in

verification procedures and capture of data for parameter identification, because they

drastically reduce the capture time and the required number of positions of the gauge used as

compared to the usual standard and manufacturer methods. These systems are also very

suitable for their capacity of capturing multiple positions of the AACMM for a single gauge

position, so that the accuracy results obtained after a procedure of identification or

verification are more generalizable than those obtained with the traditional probing systems.

The effect of auto compensation of the gauge deformation has been shown by properly

defining the trajectories of capture or the direction of probing during the process of capturing

data. Moreover, it has been demonstrated that the smallest influence of the probing force isobtained in the case of the self-centering active probe. In addition, an analysis of the influence

of the probing force over the final error was done by means of the errors vector

decomposition and by expressing this decomposition in the probed point reference system.

Furthermore, as mentioned above, since the final error depends on the combined influence

of all joints, with the presented analysis it is possible to determine on the one hand the

influence over the error of the probing itself and the relationship of that error with the

AACMM pose if there exists one, thus making possible to identify sets of joint angle values

that lead to greater probing errors. Finally, the adequacy of the self-center active probes over

self-center passive probes and spherical tip probes for tasks such as capturing data for

verification and identification of kinematics parameters has been demonstrated when no

configuration or application restrictions are imposed.

Acknowledgements

The support of Consejo Nacional de Ciencia y Tecnologa (Concayt) and Direccin

General de Educacin Superior Tecnolgica (DGEST) is deeply acknowledged by the firstand second authors. This work was supported by the DICON Innpacto Project

(IPT-2011-1191-020000), Development of new advanced dimensional control systems in

manufacturing processes of high-impact sectors. A preliminary version of the results was

presented at the XIX IMEKO World Congress Fundamental and Applied Metrology,

Performance evaluation of probing systems in data capture for kinematic parameter

Unauthenticated



13/14


identification and verification of articulated arm coordinate measuring machines, Lisbon,

Portugal, 2009.

References

[1] Santolaria, J., Brau, A., Velzquez, J., Aguilar, J. J. (2010). A self-centering active probing technique forkinematic parameter identification and verification of articulated arm coordinate measuring machines.

Meas. Sci. Technol., 21(5), 055101.

[2] Gatti, G., Danieli, G. (2008). A practical approach to compensate for geometric errors in measuring arms:application to a six-degree-of-freedom kinematic structure.Meas. Sci. Technol., 19(1), 015107.

[3] Kovac, I., Frank, A. (2001). Testing and calibration of coordinate measuring arms. Precis. Eng., 25(2),

9099.

[4] Denavit, J., Hartenberg, R. S. (1955). A kinematic notation for lower-pair mechanisms based on matrices.Trans ASME J. Appl. Mech, 23, 215221.

[5] Hayati, S., Mirmirani, M. (1985). Improving the absolute positioning accuracy of robot manipulators.J. Robot. Syst., 2(4), 397413.

[6] Elatta, A. Y., Gen, Pei L., Zhi Liang, F., Daoyuan, Y., Fei, L. (2004). An Overview of Robot Calibration.

Inf. Technol. J., 3(1), 7478.

[7] Santolaria, J., Aguilar, J., Yague, J., Pastor, J. (2008). Kinematic Parameter Estimation Technique forCalibration and Repeatability Improvement of Articulated Arm Coordinate Measuring Machines. Precis.

Eng., 32(4), 251268.

[8] Ratajczyk, E., Rak, M., Kowaluk, T. (2012). The influence of method of point collection on results with

the use of a measuring arm.Metrol. Meas. Syst., XIX(3), 541552.

[9] Everett, L., Driels, M., Mooring, B. (1987). Kinematic modelling for robot calibration.Proceedings. 1987

IEEE International Conference on Robotics and Automation, Institute of Electrical and Electronics

Engineers, 183189.

[10] Huang, C., Xie, C., Zhang, T. (2008). Determination of optimal measurement configurations for robot

calibration based on a hybrid optimal method. 2008 International Conference on Information andAutomation, 789793.

[11] Roth, Z., Mooring, B., Ravani, B. (1987). An overview of robot calibration.IEEE J. Robot. Autom., 3(5),

377385.

[12] Hamana, H., Tominaga, M., Ozaki, M., Furutani, R. (2010). Calibration of Articulated Arm CoordinateMeasuring Machine Considering Measuring Posture. 10th Internanational Symposium on Measurement

and Quality Control, 58.

[13] Piratelli-filho, A., Henrique, F., Fernandes, T., Valds, R. (2012). Application of Virtual Spheres Plate for

AACMMs evaluation.Precis. Eng., 36(2), 349355.

[14] Zheng, D., Du, C., Hu, Y. (2012). Research on optimal measurement area of flexible coordinate measuring

machines.Measurement, 45(3), 250254.

[15] Kupiec, M. (2012). Coordianate Measurment Systems Cmm and Cma Characteristc and Methods of

Their Accuracy Evaluation.Adv. Sci. Technol.Res. J., 6(16), 1723.

Unauthenticated



14/14


[16] Sadek, J., Ostrowska, K., Gska, A. (2013). Modeling and Identification of Errors of Coordinate

Measuring Arms with the Use Of A Metrological Model. Measurement, 46, 667679.

[17] Li, X. H., Chen, B., Qiu, Z. R. (2012). The Calibration and Error Compensation Techniques for an

Articulated Arm CMM with two Parallel Rotational Axes.Measurement, 46(1), 603-609.

[18] Alici, G., Shirinzadeh, B. (2005). A systematic technique to estimate positioning errors for robot accuracyimprovement using laser interferometry based sensing.Mech. Mach. Theory, 40(8), 879906.

[19] Gong, C., Yuan, J., Ni, J. (2000). Nongeometric error identification and compensation for robotic system

by inverse calibration.Int. J. Mach. Tools Manuf., 40(14), 21192137.

[20] Ali, S. H. R. (2010). Probing System Characteristics in Coordinate Metrology.Meas. Sci. Rev., 10(4), 120

129.

[21] Weckenmann, A., Estler, T., Peggs, G., McMurtry, D. (2004). Probing Systems in Dimensional Metrology.

CIRP Ann. - Manuf. Technol., 53(2), 657684.

[22] ASME B89.4.22:, (2004).Performance Evaluation of Articulated Arm Coordinate Measuring Machines.

[23] Trapet, E., Aguilar Martin, J., Yague, J., Spaan, H., Zeleny, V. (2006). Self-centering probes with parallel

kinematics to verify machine-tools.Precis. Eng., 30(2), 165179.

Documents

EVALUATION OF DIFFERENT PROBING SYSTEMS USED IN ARTICULATED.pdf